1. Field of the Invention
The present invention relates to controlling the flow of a fluid along a wall using multiple electromagnetic tiles and, more particularly, to an improved actuation technique and alternate geometry for an array of such tiles that provides extremely efficient control of the boundary layer along the wall.
2. Description of the Related Art
A viscous fluid, and a body completely immersed in the fluid, form a boundary layer at the body's surface when the fluid and the body move relative to each other. That is, the layer of fluid in contact with the body is essentially at rest, while in an area spaced from the body, the fluid moves at its free-stream velocity. The region between the body and that area is known as a boundary layer.
The boundary layer is laminar at low Reynolds' numbers. (Re=UL/.upsilon., where U is a characteristic velocity, such as the free-stream velocity, L is a characteristic dimension of the body, such as the length of a wing chord or boat hull, and .upsilon. is the kinematic viscosity of the fluid.) When the Reynolds' number increases, the boundary layer becomes unstable and turbulent. In some cases, it can "separate" from the body.
FIGS. 1(a) and 1(b) illustrate fluid flow over a body such as an airfoil. When the airfoil 10 is operating at a small angle of attack .alpha., as shown in FIG. 1(a), the fluid stream 12, with a free-stream velocity U.sub..infin., flows smoothly over the upper surface 14 of the airfoil. As the angle of attack .alpha. and/or Reynolds' number increases, the boundary layer may become turbulent, as indicated by the irregular flow 17 shown schematically in FIG. 1(b). (For purposes of illustration, the boundary layer is depicted in FIG. 1 as much thicker than it is in actuality.) At very high angles of attack the boundary layer may separate from the airfoil, which then stalls. In addition to the loss of lift caused by boundary layer separation, eddies and turbulence 18 develop in the boundary layer.
Boundary layer turbulence increases viscous drag, which may create the need for additional propulsive force, which in turn requires more fuel to be expended to maintain the speed of the airplane, submarine, propeller, etc., to which the airfoil is attached. Moreover, if the flow separates completely, additional pressure drag is created. In addition, a turbulent boundary layer exhibits large velocity and pressure fluctuations, which induce noise and vibration. FIG. 2 plots the velocity in a fluid at a wall (y=0) of a flat plate and in the region of the boundary layer. At y=0, the velocity u is generally considered to be zero. The velocity increases as y increases, and approaches the free-stream velocity U.sub..infin.. The velocity u in the mean-flow direction can thus be expressed as u(y).
The average wall shear stress .tau..sub.w in the mean-flow direction is expressed by the following relation: ##EQU1## where .mu. is the viscosity of the fluid. (The lines over the terms indicate that they represent time averages, so the equation is valid for both laminar and turbulent flow.)
In turn, the wall shear stress is related to viscous drag as follows: EQU D.sub.viscous =.intg..sub.wall .tau..sub.w dA (2)
where dA is an elemental area of the wall.
Equations (1) and (2) show that both .tau..sub.w and D.sub.viscous increase as du/dy at the wall increases.
FIG. 2 illustrates u(y) for a laminar boundary layer, shown as a solid line, and u(y) for a turbulent boundary layer, shown in a dotted line, for the same external conditions. It will be appreciated that du/dy at the wall is lower for a laminar boundary than for a turbulent boundary layer at the same location on the wall. Accordingly, viscous drag can be reduced if the flow in the boundary layer can be maintained laminar.
Various approaches have been taken to stabilize boundary layer flow and/or delay boundary layer separation. One such approach consists of optimizing the geometry of the airfoil to achieve a maximum possible angle of attack. However, even an optimum airfoil shape only allows the airfoil to operate at limited angles of attack. Another approach involves "tripping" a laminar boundary layer to cause it to become turbulent prematurely. Although that increases viscous drag, it can delay boundary layer separation.
Conventional approaches for controlling the boundary layer along a surface of an object have also included providing suction or injection of air through fine slits in the airfoil surface to supply or withdraw energy from the boundary layer. However, in addition to the burden of providing fine slits over the surface of the object, such approaches require extensive tubing networks to supply the force necessary for suction or injection. Accordingly, this approach adds considerably to the overall weight and complexity of the object, which is generally inconsistent with the design objectives of most applications (such as aircraft or submarines).
As a result, those more conventional arrangements do not achieve boundary layer control in an efficient, practical and easily implemented fashion.
On the other hand, a particularly effective boundary layer control technique, which relies on electromagnetic forces to reorganize boundary layer flow in a wholly novel manner that reduces drag, is discussed in U.S. Pat. No. 5,437,421. That technique uses multiple electromagnetic control regions, each of which is formed by North and South magnetic poles and electrodes providing an anode and a cathode, as shown in FIG. 3. FIG. 4 shows a two-dimensional array of control region tiles formed by magnets M and electrodes E, with the tiles aligned both in a direction generally along the free-stream flow direction and generally orthogonal to that direction.
In a preferred embodiment of the invention in U.S. Pat. No. 5,537,421, individual tiles in the array are actuated so that similarly situated tiles in each of multiple four-tile sub-arrays making up the entire array are actuated simultaneously. If those "equal-phase" tiles (.phi..sub.1, .phi..sub.2, .phi..sub.3, .phi..sub.4) in the sub-arrays are actuated at the proper frequency, the flow in the boundary layer is forced by the vector product L of the applied magnetic field B and electric current J in the fluid to organize into a plurality of rotational flow regions R that effect a dramatic reduction in drag.
The critical actuation frequency f.sub.crit. is determined experimentally and results in a boundary layer flow profile u(y).sub.crit. schematically shown in FIG. 5, the significance of which is explained in more detail below in connection with the detailed discussion of preferred embodiments of the present invention.
The technique described in U.S. Pat. No. 5,437,421 improved greatly over theretofore conventional boundary layer control techniques. However, it has certain drawbacks and limitations discussed in more detail below. The effort to overcome those drawbacks and limitations led to the present invention, which is an improvement over the technique of using electromagnetic forces to control boundary layer flow as disclosed in U.S. Pat. No. 5,437,421 (and related U.S. Pat. No. 5,320,309).